Reverberation is an effect of multiple reflections of sound waves. We can observe this effect when we are among a lot of tall buildings, among high mountains, or in a big hall (meeting hall or cinema hall).
We can hear the sound directly coming from the source and also from the reflections of the sound from nearby tall structures. The first reflection of sound takes some time. The further reflections of sound takes lesser and lesser time duration. They also decrease in intensity too in time.
Reverberation time is the duration for the reverberation sound to be a millionth of its intensity.
The design of big halls and auditoriums needs to take care of reverberation effect. Reverberations help the people at different locations to receive sound at uniform intensity. But we do not want to have the reverberations to last very long. An optimized value will be chosen. The wall shapes, ceiling shapes, coating or plastering on walls are done according to acoustic effects such as reverberation.